An approximation theorem for Hardy functions on $\mathbb {C}$-linearly convex domains of infinite type in $\mathbb {C}^2$
Tom 161 / 2020
Colloquium Mathematicum 161 (2020), 223-238
MSC: Primary 32A26; Secondary 32T25, 32A40.
DOI: 10.4064/cm7807-5-2019
Opublikowany online: 28 March 2020
Streszczenie
Let $\Omega \subset \mathbb {C}^2$ be a smoothly bounded, $\mathbb {C}$-linearly convex domain. We prove that if $\Omega $ is of $F$-type at all boundary points (for some type function $F$), then for all $1\le p \lt \infty $, every Hardy function $f\in H^p(\Omega )$ is approximated by a sequence of holomorphic functions on $\overline {\Omega }$ in the $H^p$-norm.
